Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data

The Performance of Binary Artificial Bee Colony (BABC) in Structure Selection of Polynomial NARX and NARMAX Models

This paper explores the capability of the Binary Artificial Bee Colony (BABC) algorithm for feature selection of Nonlinear Autoregressive Moving Average with Exogenous Inputs (NARMAX) model, and compares its implementation with the Binary Particle Swarm Optimization (BPSO) algorithm. A binarized modification of the BABC algorithm was used to perform structure selection of the NARMAX model on a Flexible Robot Arm (FRA) dataset. The solution quality and convergence was compared with the BPSO optimization algorithm. Fitting and validation tests were performed using the One-Step Ahead (OSA), correlation and histogram tests. BABC was able to outperform BPSO in terms of convergence consistency with equal solution quality. Additionally, it was discovered that BABC was less prone to converge to local minima while BPSO was able to converge faster. Results from this study showed that BABC was better-suited for structure selection in huge dataset and the convergence has been proven to be more consistent relative to BPSO

Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches

A New Proxy Measurement Algorithm with Application to the Estimation of Vertical Ground Reaction Forces Using Wearable Sensors

Measurement of the ground reaction forces (GRF) during walking is typically limited to laboratory settings, and only short observations using wearable pressure insoles have been reported so far. In this study, a new proxy measurement method is proposed to estimate the vertical component of the GRF (vGRF) from wearable accelerometer signals. The accelerations are used as the proxy variable. An orthogonal forward regression algorithm (OFR) is employed to identify the dynamic relationships between the proxy variables and the measured vGRF using pressure-sensing insoles. The obtained model, which represents the connection between the proxy variable and the vGRF, is then used to predict the latter. The results have been validated using pressure insoles data collected from nine healthy individuals under two outdoor walking tasks in non-laboratory settings. The results show that the vGRFs can be reconstructed with high accuracy (with an average prediction error of less than 5.0%) using only one wearable sensor mounted at the waist (L5, fifth lumbar vertebra). Proxy measures with different sensor positions are also discussed. Results show that the waist acceleration-based proxy measurement is more stable with less inter-task and inter-subject variability than the proxy measures based on forehead level accelerations. The proposed proxy measure provides a promising low-cost method for monitoring ground reaction forces in real-life settings and introduces a novel generic approach for replacing the direct determination of difficult to measure variables in many applications

An Indirect System Identification Technique for Stable Estimation of Continuous-Time Parameters of the Vestibulo-Ocular Reflex (VOR)

The vestibulo-ocular reflex (VOR) is a well-known dual mode bifurcating system that consists of slow and fast modes associated with nystagmus and saccade, respectively. Estimation of continuous-time parameters of nystagmus and saccade models are known to be sensitive to estimation methodology, noise and sampling rate. The stable and accurate estimation of these parameters are critical for accurate disease modelling, clinical diagnosis, robotic control strategies, mission planning for space exploration and pilot safety, etc. This paper presents a novel indirect system identification method for the estimation of continuous-time parameters of VOR employing standardised least-squares with dual sampling rates in a sparse structure. This approach permits the stable and simultaneous estimation of both nystagmus and saccade data. The efficacy of this approach is demonstrated via simulation of a continuous-time model of VOR with typical parameters found in clinical studies and in the presence of output additive noise

Comparison between Binary Particles Swarm Optimization (BPSO) and Binary Artificial Bee Colony (BABC) for nonlinear autoregressive model structure selection of chaotic data

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System Identification of Wrist Stiffness in Parkinson's Disease Patients

The purpose of this work is to investigate the characteristics of motor control systems in Parkinson's disease patients. ARMAX system identification was performed to identify the intrinsic and reflexive, the non-controllable and controllable, components of wrist stiffness, enabling a better understanding of the problems associated with Parkinson's disease. The results show that the intrinsic stiffness dynamics represent the vast majority of the total stiffness in the wrist joint and that the reflexive stiffness dynamics are attributable to a tremor commonly found in Parkinson's disease patients. It was found that Parkinsonian rigidity, a symptom of Parkinson's disease, interferes with the known and traditional methods for separating intrinsic and reflexive components. Resolving this problem could lead to early detection of Parkinson's disease in patients not exhibiting typical symptoms, analytical measurement of the severity of the disease, and as a testing mechanism for the effectiveness of new medicines